Long-distance radiative excitation transfer between quantum dots in disordered photonic crystal waveguides

Abstract

We theoretically investigate the magnitude and range of the photon-mediated interaction between two quantum dots embedded in a photonic crystal waveguide, including fabrication disorder both in the crystal and in the dot positioning. We find that disorder-induced light localization has a drastic effect on the excitation transfer rate-as compared to an ideal structure-and that this rate varies widely among different disorder configurations. Nevertheless, we also find that significant rates of 50 μeV at a range of 10 μm can be achieved in realistic systems. Semiconductor quantum dots (QDs) have very recently become candidate building blocks of a quantum-information technology, after the experimental proof of full single-qubit control. [1][2][3][4][5][6][7][8] Beyond that, the possibility for two qubits to interact coherently in a controlled fashion is an essential requirement for two-qubit quantum gates, which are a building block of the mainstream quantum-information protocol. 9Given the localized nature of the quantum dots, a quantum bus is needed to provide the link between distant QD qubits. 10In a semiconductor system, photons are an obvious choice for this task, due to their weak coupling to the environment (long decoherence time), and long-distance propagation. Additionally, semiconductor photonic crystal (PHC) devices have advanced to a remarkable level of sophistication. The state-of-the-art subnanometer fabrication precision 11-13 has brought about ultra-high-Q cavity designs [14][15][16] with mode volumes close to the diffraction limit, as well as low-loss, slow-light engineered waveguides. 17 This, together with the recent experimental success of Purcell-enhancing the emission of a single dot in a PHC waveguide, [18][19][20][21][22][23] and even reaching the strong coupling regime in such a structure, 24 suggests that a PHC-QD system could be an ideal candidate for demonstrating photon-mediated excitation transfer between distant dots.Coherent interaction between two QDs at subwavelength distance in a microcavity has been recently observed. 25 At longer distance, the interaction was theoretically shown to be finite but weak (as compared to typical radiative loss and decoherence rates) in three-dimensional (bulk) 26 and twodimensional 27 spatially homogeneous dielectric environments. The ideal compromise between interaction strength and range is thus expected in a one-dimensional environment like a PHC waveguide, and indeed, the possibility for entangled states between distant QDs coupled to such a structure has been demonstrated, 28 and the characteristic interaction distance was estimated 29 to be given by r 12 = 2v g /γ , where v g is the group velocity at the exciton resonant frequency, while γ is the loss rate of the waveguide modes. However, it is known that disorder residual in the fabrication process dramatically affects the slow-light guided modes. In Ref. 29, we partially took this into account by introducing a phenomenological loss rate γ as stemming from disorder-induced (extrinsic) losses, ...

Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections

“…As such, they are not easy to handle in applications that require extreme precisions, but their existence and the possibility to enhance (statistically) their spatial confinement by using flatter dispersion curves is extremely relevant for quantum electrodynamics experiments14151617, random lasing1819, but also for sensing applications5354 and random photonics devices5556.…”

“…Besides these works, the research topic arose considerable interest in the photonic-crystal community, when it was realized that the operation of slow-light devices based on photonic-crystal waveguides (PhCWs) was unavoidably limited by small residual fabrication imperfections 10 11 12 13 . The possibility to observe individual localized modes formed by disorder in these structures and exploit them as “optical cavities” for, e.g., quantum information processing 14 15 16 17 or random lasing 18 19 prompted numerous studies on their confinement properties 20 21 22 23 . Quite remarkably, near-field measurements on PhCWs fabricated with state-of-the-art nanotechnologies 22 23 suggest that wavelength-scale localized modes, comparable in size to engineered heterostructure nanocavity modes in PhCWs 24 25 , could naturally be formed in spite of the very low perturbation level.…”

Statistics of Anderson-localized modes in disordered photonic crystal slab waveguides

“…Intrinsic disorder can be introduced by fluctuating either the hole positions 29,33 or sizes 45 , or even both 38,40 , and more sophisticated models can be also introduced to take into account the hole roughness 46,47 . We consider fluctuations in the hole positions as the main intrinsic disorder contribution and set σ i = 0.005a in all our calculations, corresponding to the state-of-art in GasAs/InGaAs fabrication techniques 33 .…”

Long-distance radiative coupling between quantum dots in photonic crystal dimers

“…The role of disorder on light localization was also addressed [25]. Alternatively, preliminary studies considered the mutual coupling between two QDs positioned at the field antinodes within the same PC cavity [24,26], for which early experimental evidence was shown [27].…”